Conventionally, an internal combustion engine is provided with a gas sensor such as an A/F sensor, an O2 sensor, which detects oxygen concentration, a NOx sensor, which detects nitrogen oxide concentration, and the like. In such an internal combustion engine, for example, fuel injection quantity is controlled based on a detection signal of the gas sensor so as to reduce emission contained in exhaust gas of the engine. Such a gas sensor is provided with a heater for heating a sensor element so as to activate the sensor element in a starting operation of the internal combustion engine, for example. The heater is configured to quickly activate the sensor element so as to enhance reduction in emission in the starting operation of the engine. In such a gas sensor, failure such as short circuit of both wiring ends of the heater, disconnection of the heater, and the like may arise in a circuit for supplying electricity to the heater. For example, U.S. Pat. No. 6,164,125 (JP-A-11-6812) discloses a gas sensor system, which determines the short circuit and the disconnection. Specifically, in the gas sensor system, when monitoring voltage between both wiring ends of the heater is lower than a threshold VTHα (FIG. 4), it is determined that disconnection arises. Alternatively, when the monitoring voltage is higher than a threshold VTHβ (FIG. 4), it is determined that short circuit arises. In recent years, reduction of emission is increasingly demand. Therefore, detection of degradation caused by aging of the heater is also demanded in addition to detection of the short circuit and the disconnection of the heater.